Finite Group Databasebeta

← #34098685

Subgroups — #34098685

Order 20096.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757825C211yesmaximal, characteristic
2#23757327C211yesmaximal, characteristic
3#23757140C211yesmaximal, characteristic
4#23757011C211yesmaximal, characteristic
5#23757010C211yesmaximal, characteristic
6#23757009C211yesmaximal, characteristic
7#328×C157C211yesmaximal, characteristic
8#19097770C411yescharacteristic, complemented
9#19097769C411yescharacteristic, complemented
10#19097761—21no—
11#19097750C2211yescharacteristic
12#19097748—21no—
13Q8×Dic157C411yescharacteristic, complemented
14#19097736—21no—
15#19097736C411yescharacteristic, complemented
16#19097727—21no—
17C2×C4×Dic157C2211yescharacteristic
18#19097700—21no—
19C22⋊#11929434C2211yescharacteristic
20#19097681—21no—
21#19097678—21no—
22#19097678—21no—
23#19097678C2211yescharacteristic
24C22⋊Q8×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314C2×C411yescharacteristic
29C22×Dic157—21no—
30C22×Dic157D411yescharacteristic
31C22×Dic157D411yescharacteristic
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157C2×C411yescharacteristic
35#14578933—21no—
36#14578933—21no—
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40C22⋊Dic157—21no—
41C4×Dic157—21no—
42C4×Dic157—21no—
43C4×Dic157C2×C411yescharacteristic
44C4×Dic157C2×C411yescharacteristic
45C4×Dic157D411yescharacteristic
46C4×Dic157D411yescharacteristic
47C2×Q8×C157C2×C411yescharacteristic
48C22×C4×C157—21no—
49C22×C4×C157C2311yescharacteristic
50C2×C8×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157C2×C411yescharacteristic
53C22⋊C4×C157—21no—
54Dic314—42no—
55Dic314—41no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—21no—
60C2×Dic157—41no—
61C2×Dic157—41no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157C22⋊C411yescharacteristic
65C2×Dic157C22⋊C411yescharacteristic
66C2×Dic157C22⋊C411yescharacteristic
67C2×Dic157C22⋊C411yescharacteristic
68#11929434—41no—
69C23×C157C2×D411yescharacteristic
70Q8×C157—41no—
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157C22×C411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C8×C157—41no—
80C22×C157—21no—
81C22×C157—21no—
82C22×C157C2×C22⋊C411yescharacteristic
83C22×C157#13711yescharacteristic
84C22×C157#13711yescharacteristic
85C4×C157—21no—
86C4×C157—21no—
87C4×C157—41no—
88C4×C157—41no—
89C4×C157—81no—
90Dic157—21no—
91Dic157—21no—
92Dic157—21no—
93Dic157—21no—
94Dic157—41no—
95Dic157—41no—
96Dic157—81no—
97C2×C157—21no—
98C2×C157—21no—
99C2×C157#41011yescharacteristic
100C2×C157#41911yescharacteristic
101C2×C157#42111yescharacteristic
102C157#151511yescharacteristic, complemented, Sylow
103#1515—1571nomaximal, Sylow
104#533—1571no—
105#432—1571no—
106#383—1571no—
107#328—1571no—
108#328—1571no—
109#328—1571no—
110#328D15711yescharacteristic
111C4⋊Q8—1571no—
112C4⋊Q8—1571no—
113#125—3141no—
114C22⋊Q8—3141no—
115C22⋊Q8—1571no—
116C22⋊Q8C2×D15711yescharacteristic
117C4×Q8—3141no—
118C4×Q8—1571no—
119C4×Q8—1571no—
120#117—3141no—
121C2×C42—1571no—
122C4⋊C8—3141no—
123C22⋊C8—1571no—
124C22⋊C8C2×D15711yescharacteristic
125#97—3141no—
126#95—3141no—
127#95—3141no—
128#95—1571no—
129#95C2×D15711yescharacteristic
130C2×Q8—3141no—
131C2×Q8—1571no—
132C2×Q8C4×D15711yescharacteristic
133C22×C4—21no—
134C22×C4—3141no—
135C22×C4—1571no—
136C22×C4—1571no—
137C22×C4C22×D15711yescharacteristic
138C2×C8—21no—
139C2×C8—3141no—
140C4⋊C4—21no—
141C4⋊C4—3141no—
142C4⋊C4—3141no—
143C4⋊C4—3141no—
144C4⋊C4—3141no—
145C4⋊C4—3141no—
146C4⋊C4—3141no—
147C4⋊C4—1571no—
148C4⋊C4C4×D15711yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—3141no—
151C42—3141no—
152C42—3141no—
153C42—1571no—
154C42—1571no—
155C42—1571no—
156C42—1571no—
157C23D4×D15711yescharacteristic
158Q8—41no—
159Q8—6281no—
160Q8—6282no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—3141no—
168C2×C4—3141no—
169C2×C4—3141no—
170C2×C4—3141no—
171C2×C4—6281no—
172C2×C4—6281no—
173C2×C4—6281no—
174C2×C4—6281no—
175C2×C4—1571no—
176C2×C4—1571no—
177C2×C4—1571no—
178C2×C4—1571no—
179C2×C4C2×C4×D15711yescharacteristic
180C2×C4D4×D15711yescharacteristic
181C8—41no—
182C8—6281no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D15711yescharacteristic
186C22#1909780011yescharacteristic
187C22#1909780311yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—3141no—
194C4—3141no—
195C4—3141no—
196C4—3141no—
197C4—6281no—
198C4—6281no—
199C4—12561no—
200C2—21no—
201C2—21no—
202C2#2375724511yescharacteristic
203C2#2375728011yescharacteristic
204C2#2375728811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#328×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC23×C157C2×D4
cosocleC22×C4×C157C23
hypercenter#328D157
hypocenterC157#1515
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
8. #19097770C4semidirect
9. #19097769C4semidirect
13. Q8×Dic157C4semidirect
15. #19097736C4semidirect
102. C157#1515semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237578252
#237573272
#237571402
#237570112
#237570102
#237570092
#328×C1572
#1515157